Precise Square Roots by Hand Tutorial

also thanks to Lucia my marvelous thumbnail artist

This video was inspired by Matt Parkers video on the Chudnovsky algorithm. He calculated root 10005 by hand, so I improved on the method and created my own root algorithm. This happened over 2 years ago. Since the algorithm isn't hard to remember (2z²-p²)÷(2zn) I still know it, but I forgot how I proved that it worked. Now in quarantine I tried to reconstruct my proof, but just was unable to do it.